In a cellular system implementing a third generation mobile network technology compliant with the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) standard (document 3GPP TS 36.211 V9.1.0 (2010-03)), pseudo-random sequences are defined by a length-31 Gold sequence (section 7.2 of document 3GPP TS 36.211 V9.1.0 (2010-03)). The output sequence c(n) of length MPN, where n=0, 1, . . . , MPN−1, is defined by the following equations:c(n)=(x1(n+NC)+x2(n+NC))mod 2  Eq. 1x1(n+31)=(x1(n+3)+x1(n))mod 2,  Eq. 2x2(n+31)=(x2(n+3)+(x2(n+2)+x2(n+1)+x2(n))mod 2.  EQ. 3The term NC represents a constant having a value of 1600. The terms x1(n+NC) and x2(n+NC) are referred to as a first m-sequence and a second m-sequence, respectively. The first m-sequence is initialized with x1(0)=1, x1(n)=0, n=1, 2, . . . , 30. The initialization of the second m-sequence is denoted by the following equation:
                              c          init                =                              ∑                          i              =              0                        30                    ⁢                                          ⁢                      x            ⁢                                                  ⁢            2            ⁢                                          (                i                )                            ·                                                2                  i                                .                                                                        EQ        .                                  ⁢        4            The initialization value of the second m-sequence depends on the application of the pseudo-random sequence.
When samples c(0), c(1), . . . , c(31) are available, the sequence can be calculated easily. However, the samples c(0), c(1), . . . , c(31) have to be calculated based on the initialization sequence of x2 and x1. While the initialization sequence of x1 is constant and, therefore, can be pre-calculated, the sequence for x2(1600), . . . , x2(1630) should be calculated for each different application of the pseudo-random sequence. In a conventional system, the samples x2(1600), . . . , x2(1630) are calculated directly by iteratively calculating x2(0) through x2(1600) using Equation 4 above. The main disadvantage of the conventional method is that calculating 1600 samples utilizes real-time resources of the system and can create real-time problems.
It would be desirable to have a method and/or apparatus for implementing a fast calculation of the beginning of pseudo random sequences for LTE.